And Flocculation

Mixing is a unit operation that distributes the components of two or more materials among the materials producing in the end a single blend of the components. This mixing is accomplished by agitating the materials. For example, ethyl alcohol and water can be mixed by agitating these materials using some form of an impeller. Sand, gravel, and cement used in the pouring of concrete can be mixed by putting them in a concrete batch mixer, the rotation of the mixer providing the agitation.

Generally, three types of mixers are used in the physical-chemical treatment of water and wastewater: rotational, pneumatic, and hydraulic mixers. Rotational mixers are mixers that use a rotating element to effect the agitation; pneumatic mixers are mixers that use gas or air bubbles to induce the agitation; and hydraulic mixers are mixers that utilize for the mixing process the agitation that results in the flowing of the water.

Flocculation, on the other hand, is a unit operation aimed at enlarging small particles through a very slow agitation of the water suspending the particles. The agitation provided is mild, just enough for the particles to stick together and agglomerate and not rebound as they hit each other in the course of the agitation. Floccu-lation is effected through the use of large paddles such as the one in flocculators used in the coagulation treatment of water.

6.1 rotational mixers

Figure 6.1 is an example of a rotational mixer. This type of setup is used to determine the optimum doses of chemicals. Varying amounts of chemicals are put into each of the six containers. The paddles inside each of the containers are then rotated at a predetermined speed by means of the motor sitting on top of the unit. This rotation agitates the water and mixes the chemicals with it. The paddles used in this setup are, in general, called impellers. A variety of impellers are used in practice.

6.1.1 Types of Impellers

Figure 6.2 shows the various types of impellers used in practice: propellers (a), paddles (b), and turbines (c). Propellers are impellers in which the direction of the driven fluid is along the axis of rotation. These impellers are similar to the impellers used in propeller pumps treated in a previous chapter. Small propellers turn at around 1,150 to 1,750 rpm; larger ones turn at around 400 to 800 rpm. If no slippage occurs between water and propeller, the fluid would move a fixed distance axially. The ratio of this distance to the diameter of the impeller is called the pitch. A square pitch is one in which the axial distance traversed is equal to the diameter of the propeller. The pitching is obtained by twisting the impeller blade; the correct degree of twisting induces the axial motion.

6 Mixing

FIGURE 6.1 An example of a rotational mixer. (Courtesy of Phipps & Bird, Richmond, VA. © 2002 Phipps & Bird.)

FIGURE 6.2 Types of impellers. (a) Propellers: (1) guarded; (2) weedless; and (3) standard three-blade. (b) Paddles: (1) pitched and (2) flat paddle. (c) Turbines: (1) shrouded blade with diffuser ring; (2) straight blade; (3) curved blade; and (4) vaned-disk.

FIGURE 6.2 Types of impellers. (a) Propellers: (1) guarded; (2) weedless; and (3) standard three-blade. (b) Paddles: (1) pitched and (2) flat paddle. (c) Turbines: (1) shrouded blade with diffuser ring; (2) straight blade; (3) curved blade; and (4) vaned-disk.

Figure 6.2(a)1 is a guarded propeller, so called because there is a circular plate ring encircling the impeller. The ring guides the fluid into the impeller by constraining the flow to enter on one side and out of the other. Thus, the ring positions the flow for an axial travel. Figure 6.2(a)2 is a weedless propeller, called weedless, possibly because it originally claims no "weed" will tangle the impeller because of its two-blade design. Figure 6.2(a)3 is the standard three-blade design; this normally is square pitched.

Figure 6.2(b) 1 is a paddle impeller with the two paddles pitched with respect to the other. Pitching in this case is locating the paddles at distances apart. Three or four paddles may be pitched on a single shaft; two and four-pitched paddles being more common. The paddles are not twisted as are the propellers. Paddles are so called if their lengths are equal to 50 to 80% of the inside diameter of the vessel in which the mixing is taking place. They generally rotate at slow to moderate speeds of from 20 to 150 rpm. Figure 6.2(b)2 shows a single-paddle agitator.

Impellers are similar to paddles but are shorter and are called turbines. They turn at high speeds and their lengths are about only 30 to 50% of the inside diameter of the vessel in which the mixing is taking place. Figure 6.2(c) 1 shows a shrouded turbine. A shroud is a plate added to the bottom or top planes of the blades. Figures 6.2(c)2 and 6.2(c)3 are straight and curve-bladed turbines. They both have six blades. The turbine in Figure 6.2(c)4 is a disk with six blades attached to its periphery.

Paddle and turbine agitators push the fluid both radially and tangentially. For agitators mounted concentric with the horizontal cross section of the vessel in which the mixing is occurring, the current generated by the tangential push travels in a swirling motion around a circumference; the current generated by the radial push travels toward the wall of the vessel, whereupon it turns upward and downward. The swirling motion does not contribute to any mixing at all and should be avoided. The currents that bounce upon the wall and deflected up and down will eventually return to the impeller and be thrown away again in the radial and tangential direction. The frequency of this return of the fluid in agitators is called the circulation rate. This rate must be of such magnitude as to sweep all portions of the vessel in a reasonable amount of time.

Figure 6.3 shows a vaned-disk turbine. As shown in the elevation view on the left, the blades throw the fluid radially toward the wall thereby deflecting it up and down.

FIGURE 6.3 Flow patterns in rotational mixers.

The arrows also indicate the flow eventually returning back to the agitator blades— the circulation rate. On the right, the swirling motion is shown. The motion will simply move in a circumference unless it is broken. As the tangential velocity is increased, the mass of the swirling fluid tends to pile up on the wall of the vessel due to the increased centrifugal force. This is the reason for the formation of vortices. As shown on the left, the vortex causes the level of water to rise along the vessel wall and to dip at the center of rotation.

6.1.2 Prevention of Swirling Flow

Generally, three methods are used to prevent the formation of swirls and vortices: putting the agitator eccentric to the vessel, using a side entrance to the vessel, and putting baffles along the vessel wall. Figure 6.4 shows these three methods of prevention. The left side of Figure 6.4a shows the agitator to the right of the vessel center and in an inclined position; the right side shows the agitator to the left and in a vertical position. Both locations are no longer concentric with the vessel but eccentric to it, so the circumferential path needed to form the swirl would no longer exist, thus avoiding the formation of both the swirl and the vortex.

Figure 6.4b is an example of a side-entering configuration. It should be clear that swirls and vortices would also be avoided in this kind of configuration. Figure 6.4c shows the agitator mounted at the center of the vessel with four baffles installed on the vessel wall. The swirl may initially form close to the center. As this swirl

FIGURE 6.4 Methods of swirling flow prevention.

propagates toward the wall, its outer rim will be broken by the baffles, however, preventing its eventual formation.

6.1.3 Power Dissipation in Rotational Mixers

A very important parameter in the design ofmixersisthepowerneededtodriveit. This power can be known if the power given to the fluid by the mixing process is determined. The product of force and velocityispower.Givenaparcelof water administered a push (force) by the blade,theparcelwillmoveandhenceattain a velocity, thus producing power. The force existsaslongasthepush exists;however, the water will not always be in contact withtheblade;hence,thepushingforcewill cease. The power that the parcel had acquired will therefore simply be dissipated as it overcomes the friction imposed by surrounding parcels of water. Power dissipation is power lost due to frictional resistanceandisequaltothepowergivento it by the agitator.

Let us derive this power dissipation by dimensional analysis. Recall that in dimensional analysis pi groups are to be found that are dimensionless. The power given to the fluid should be dependent onthe variousgeometricmeasurementsof the vessel. These measurements can be conveniently normalized against the diameter of the impeller Da to make them into dimensionless ratios. Thus, as far as the geometric measurements are concerned, they have now been rendered dimensionless. These dimensionless ratios are called shape factors.

Refer to Figure 6.5. As shown, there are seven geometric measurements: W, the width of the paddle; L, the length of the paddle; J,, the width of the baffle; H, the depth in the vessel; D„ the diameter of the vessel; E, the distance of the impeller to the bottom of the vessel; and Da, the diameter of the impeller. The corresponding shape factors are then S1 = W/D, S2 = L/D, S3 = J/Da, S4 = H/Da, S5 = Dt/Da, and S6 = E/Da. In general, if there are n geometric measurements, there are n - 1 shape factors.

The power given to the fluid should also be dependent on viscosity f, density p, and rotational speed N. The higher the viscosity, the harder it is to push the fluid, increasing the power required. A similar argument holds for the density: the denser w w h

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